Are there any hotels close to the airport? We are trying to find economical fares, but everything that's economical seems to get us in at about 8:30. We thought this wouldn't be too bad if we can find something close to the airport for 1 night.

We will be staying at the Sea Aquarium, so another thought was to grab a taxi and go to the otherside of the island when we arrive. Do the taxis run this late?

Hotel Holland lies practially next to the airport, you can watch the planes on the runway from the terrace.
But I guess you are miscalculating the distances on CuraĆ§ao: by cab/taxi it is less than half an hour drive to Seaquarium. So it is not necessary to book a hotel at the airport at all!
Els

leaving the airport, turn right. At the roundabout, straight on. At the second roundabout, also straight on, till the last trafficlights before the harbour (on your right there is a large, empty lot). There you turn left in the direction of Punda, this is the road to the high Juliana bridge. Keep the left lain.
After passing the bridge, just straight on till you see the traffic lights with KFC at one and MacDonald on the other corner. Turn right here, at the roundabout make a almost 180 degrees and then left (this is the first left, not the second) in the direction of the traffic lights you see about 400 meters further.
At these trafficlights, turn right. Follow this road to the end (you can see the ocean now), turn left and follow the road till the end, where you will find the Seaquarium and Lions Dive Hotel.
Have a nice trip.
Els